Charron-Bost and
Schiper [1]} define it as the heard-of predicate of
the synchronous version of this model. To prove it, we would need a formal definition
of the delivered predicate for a given model. This is hard because operational
models are rarely formal and the best we can do is to give an informal argument for why,
if you take the asynchronous model with reliable communication and at most \(F\) 
permanent crashes, and implement communication-closed rounds in any way that
ensures an infinite number of rounds for every process, the messages received
will form a delivered collection of \(\textit {DEL}^{crash}_F\) .
In the other direction, every collection of \(\textit {DEL}^{crash}_F\)  captures
the message received in an execution of the implementation of rounds on top
of the aforementioned asynchronous model.
